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Acta Physica Polonica B

SOME NEW DEVELOPMENTS IN NONLINEAR OPTICS

Marek Trippenbach, E. Infeld

Published Mar 1, 2006• 0 citations
OpenAlex

Abstract

Soltan Institute for Nuclear Studies, Hoza 69, 00-681 Warsaw, Poland(Received January 16, 2006)We review some new developments in modern nonlinear optics. Theyare related to optics with both photons and atoms. The goals of the pre-sentation were to give a cursory review on contemporary challenges in non-linear optics (focusing on problems that are of interest to the Warsaw non-linear optics group) and to show how fruitful it can be to transfer ideasacross the border between different fields.PACS numbers: 03.75.Fi, 42.65.Tg

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Soltan Institute for Nuclear Studies, Hoza 69, 00-681 Warsaw, Poland(Received January 16, 2006)We review some new developments in modern nonlinear optics. Theyare related to optics with both photons and atoms. The goals of the pre-sentation were to give a cursory review on contemporary challenges in non-linear optics (focusing on problems that are of interest to the Warsaw non-linear optics group) and to show how fruitful it can be to transfer ideasacross the border between different fields.PACS numbers: 03.75.Fi, 42.65.Tg
In 2016 we published a review paper "Nonlinear and Quantum Optics with Whispering Gallery Resonators" (1). While writing this review, we found it often necessary to defer addressing many challenges of the field to the future. At the same time, many potential benefits offered by nonlinear optical resonators were also deferred to the future pending the underlying technology development. The past ten years have seen a great deal of such development, including in the field of resonator optics. We feel that an update to our 2016 review is in order. In this new review we focus on the most significant developments in the field that took place in past ten years.
This is a challenging paper that includes some reviews and new results. Since the non-commutative version of the classical system based on the compact group SU(2) has been constructed in (quant-ph/0502174) by making use of Jaynes–Commings model and so-called quantum diagonalization method in (quant-ph/0502147), we construct a non-commutative version of the classical system based on the non-compact group SU(1,1) by modifying the compact case. In this model the Hamiltonian is not hermite but pseudo hermite, which causes a big difference between the two models. For example, in the classical representation theory of SU(1,1), unitary representations are infinite dimensional from the starting point. Therefore, to develop a unitary theory of non-commutative system of SU(1,1) we need an infinite number of non-commutative systems, which means a kind of second non-commutativization. This is a very hard and interesting problem. We develop a corresponding theory though it is not always enough, and present some challenging problems concerning how classical properties can be extended to the non-commutative case. This paper is arranged for the convenience of readers as the first subsection is based on the standard model (SU(2) system) and the next one is based on the non-standard model (SU(1,1) system). This contrast may make the similarities and differences between the standard and non-standard models clearer.
We compute the stationary profiles of a coherent beam of Bose condensed atoms propagating through a guide. Special emphasis is put on the effect of an obstacle present on the trajectory of the beam. The obstacle considered (such as a bend in the guide, or a laser field perpendicular to the beam) results in a repulsive or an attractive potential acting on the condensate. Different behaviors are observed when varying the beam velocity (with respect to the speed of sound), the size of the obstacle (relative to the healing length) and the intensity and sign of the potential. The existence of bound states of the condensate is also considered. PACS numbers: 03.75.b Matter waves 03.75.Fi Phase coherent atomic ensembles; quantum condensation phenomena 42.65.Tg Optical solitons; nonlinear guided waves 67.60.Hf Hydrodynamics in specific geometries, flow in narrow channels 1 Unité Mixte de Recherche de l’Université Paris XI et du CNRS (UMR 8626).